Long Range Potential Effects in Low Density Krypton Gas

Abstract

Small angle neutron scattering (SANS) in low density 86 Kr gas has been performed in order to measure the small-k behavior of the static structure factor S͑k͒. Three number densities between 1.52 and 2.42 nm 23 along the T 297 K isotherm have been studied. The small-k dependence of the Fourier transform c͑k͒ of the direct correlation function c͑r͒ has been derived. The experimental determination of the k 3 term in the behavior of c͑k͒ has led to a direct measurement of the London dispersion interaction in the pair potential of krypton. Also the contribution of the three-body potential in the asymptotic behavior of c͑r͒ has been observed and related to the magnitude of the three-body interaction potential.[ S0031-9007(97) The London dispersion energy due to the induced dipole interactions determines the form of the long range potential of pairs, as well as the form of the long range irreducible three-body interaction in ground state atoms [1,2]. One possibility for a direct assessment of these long range interactions among the particles in a fluid is given by the connection between the small-k behavior of the static structure factor S͑k͒ [Eq. (1) below] and the long range microscopic forces. This connection has been pointed out by Enderby, Gaskell, and March [3], who emphasized the importance of direct observation of such terms. Several papers have been devoted to this subject [4][5][6], and recently this matter has been discussed by Reatto and Tau [7]. The main result of these papers is that for classical fluid insulators, like noble gases, S͑k͒ and c͑k͒ [Eq. (2) below], which is the Fourier transform of the direct correlation function c͑r͒, are expected to have at small k a nonanalytic k 3 term directly related to the r 26 tail of the microscopic van der Waals interaction potential in the fluid. In particular, the theory of Reatto and Tau [7] takes into account the effect of retardation which modifies k 3 to k 4 as k ! 0. Moreover, they confirm that measurements of the k 3 behavior of c͑k͒ in low density gases can, in principle, give an experimental direct verification of the r 26 power law of the pair potential and might determine the long range behavior of the dressed three-body vertex. However, we shall show that in the present case the k 2 term includes a larger and more useful measure of the dressed three-body vertex, giving a direct and unique experimental access to the long range interaction.Neutron diffraction measurements, when possible with high accuracy, have been proven to be a direct method for the determination of the interaction potential between pairs of atoms in gases [8,9]. Recently, both normal diffraction and SANS experiments have been performed in argon gas in order to measure the k 3 dependence of c͑k͒ and give an experimental value of the amplitude B of the long range 2B͞r 6 pair potential [10,12] in agreement with that determined by more traditional methods. Here we report the results of the measurements of the smallk dependence of the c͑k͒ of krypton at low density from which the stren...

Long-range interactions in insulating fluids probed by SANS

“…In Kr and Xe many-body effects, which are connected to the polarizability of the system, are expected to be more pronounced. This has been actually confirmed in further experiments carried out at 297 K and several low densities in gaseous Kr (Formisano, Benmore, Bafile, Barocchi, Egelstaff, Magli & Verkerk, 1997, Benmore, Formisano, Magli, Bafile, Verkerk, Egelstaff & Barocchi, 1999 and Xe (Formisano, Barocchi & Magli, 1998). In Fig.…”

Collective dynamics and molecular interactions in liquidCO2by inelastic neutron scattering and computer simulations

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Three-body dispersion contributions to the thermodynamic properties and effective pair interactions in liquid argon

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